Long tail monetization procedure

ABSTRACT

A system and method for constructively providing a monetization procedure for a long tail demand curve of market goods, services or contents through a channel such as the Internet or mobile devices, for which there exists a source providing economic scoring (sales, downloads, streaming hours, etc.). Using only the scorings for a few reference items and a quantitative concept of similarity between the items, embodiments provide a procedure that constructively distributes the score from the reference items to the non-ranked ones, yielding the full scoring curve adjusted to a long tail law (power law). In order to build scores for non-ranked items, the method recursively defines relative preferences between items based on their similarity, thus constructing a utility-like function. The preferences are then used within an iterative tournament strategy between the items.

CROSS REFERENCES TO RELATED APPLICATION

The present application claims the benefit under 35 U.S.C. §120 as anon-provisional of presently pending U.S. Patent Application Ser. No.61/512,657 entitled “LONG TAIL MONETIZATION PROCEDURE”, filed on Jul.28, 2011, the entire teachings of which are incorporated herein byreference.

BACKGROUND

1. Field of the Invention

The present invention relates to the problem of modeling the scoring ordemand curves for large sets of objects (products or downloads), incases where the demand behavior is known to exhibit the Long Tailphenomenon. This is particularly relevant in the context ofInternet-based commerce, where various businesses have beenexperimentally proven to behave that way. In particular, the methodconcentrates on the problem of predicting the full scoring curve usingincomplete information. The method works with the scoring values of justa few (reference) objects, plus some quantified measure of similaritybetween all the objects.

2. Description of the Background

The concept of a “long tail” distribution has been commonly used indiverse fields, like statistics and physics, to refer to phenomena inwhich the distribution of a magnitude is shown to exhibit a power-lawdecay as the magnitude approaches very large values. For the purposes ofthis discussion, power-law decaying distributions are special mainlybecause of the much slower rate of decay as compared with Gaussiandistributions, for example. However, power laws are also special becausethey show scale-free behavior, meaning that the shape of the curve canbe easily rescaled to fit a common (i.e. “universal”) power law of thetype x^(α). In other words, the exponent α is all that characterizes thedistribution curve for large x.

In the context of the new Internet-based economy, the popularization ofthe concept of “The Long Tail” is attributed to Chris Anderson. In hisfirst article in Wired Magazine (Anderson, “The Long Tail”, Wired, Issue12.10, October 2004) and then later in his book (Anderson, “The LongTail: Why the Future of Business Is Selling Less of More” (New York:Hyperion Press 2006)), Anderson shows how, for most of the new bigInternet retailers, the demand exhibits a long tail behavior. Note thatthis actually concerns the demand curve for the universe of items onsale, when these are ordered by sales rank. Although it may be temptingto think of it as a “probability distribution” for the number of sales,this could be misleading and lead to wrong analyses. Notwithstanding afew criticisms (notably, Tan et al., “Is Tom Cruise Threatened? UsingNetflix Prize Data to Examine the Long Tail of Electronic Commerce”,July 2009, Wharton, University of Pennsylvania, available athttp://opim.wharton.upenn.edu/˜netessin/TanNetessine.pdf), it is widelyrecognized that the tenets of the theory are experimentally confirmedboth for large and small retailers (see Bailey et al., “The Long Tail isLonger than You Think: The Surprisingly Large Extent of Online Sales bySmall Volume Sellers, May 13, 2008, available at SSRN:http://ssrn.com/abstract=1132723).

The mechanisms by which the long tail behavior appears are well known:the new era of on-line retail allows businesses to enlarge their productcatalog endlessly, because shelf-space costs are nearly zero. Onceconsumers are offered limitless variety, it is to be expected that thedemand curves extend their shape to more and more items. However, thenon-obvious aspect of the theory is that the particular shape of thetail is a power-law tail (see FIG. 1). The implications for businessmodels are then clear: an internet business can now monetize the tail ofthe long tail distribution of the demand. Moreover, the demand in thewhole tail can actually add up to a percentage of sales that rivals thehead of the curve (see FIG. 2). Today, it is evident that the mostsuccessful Internet businesses have been those with the vision andskills to monetize the long tail of the demand (see, for instance, Levy,“In the Plex: How Google thinks, works, and shapes our lives” (Simon &Schuster 2011)).

Therefore, it has become quite important to accurately model and predictthe long tail part of a demand curve, in order to optimize the economicvalue extracted from it. Such modeling enables better quantification oftargeted marketing or recommendation system efforts. Although the longtail framework is quite recent, many publications and innovations makeuse of it in one way or another.

U.S. Patent App. Pub. No. 2007/0294733 by Aaron et al. describes methodsfor facilitating content-based selection in long tail business models,based on the position of the requested item on a content demand curve.

Another area of interest is that of destroying or minimizing anyremaining barriers to a full long tail business; in other words, ensurethat the shelving costs remain close to zero. For instance, in U.S. Pat.No. 6,223,205 granted to Harchol-Balter et al., a method is disclosedfor assigning tasks in a distributed server system, intended to optimizerequests for service in the scenario of heavy tailed distributions. U.S.Pat. No. 7,707,215 granted to Huberman et al. describes a pari-mutuelcontent provisioning method for peer-to-peer networks, intended toprovide a wide diversity of content offerings while respondingadaptively to customer demand. Files are served and paid for through apari-mutuel market (similar to that commonly used for betting in horseraces), and it is shown that the system achieves an equilibrium with along tail in the distribution of content offerings, guaranteeing thereal-time provision of any content regardless of its popularity.

U.S. Pat. No. 7,720,933 granted to Gordon et al. discloses an end-to-enddata transfer method in which a multi-tiered control system combines thebest features of a centralized system and peer-to-peer systems in orderto minimize the problems associated with serving “obscure” content (thefar end of the long tail distribution, i.e. non-popular or less soldcontents). U.S. Patent App. Pub. No. 2010/0332595 by Fullagar et al.also deals with the problems related to handling long tail content in adelivery network. It discloses a method consisting of a hierarchy ofservers designed to cache a universe of items with a long tailed demandcurve.

U.S. Pat. No. 7,647,332 to Van Flandern et al. shows methods to dealwith the problem of content discovery in the context of abundant longtail commerce, in the form of an aggregating interface.

A different set of problems includes those related to the prediction ofthe scoring of particular items, and the related problem of itemsimilarity. Targeted marketing campaigns and recommendation systems makeuse of these two key concepts; therefore, they are crucial for thesuccessful exploitation of long tail markets. See for instance,Ardissono et al., “User Modeling and Recommendation Techniques forPersonalized Electronic Program Guides”, pp. 3-26 in: PersonalizedDigital Television, Human-Computer Interaction Series Vol. 6, Eds.Ardissono et al., Springer, Netherlands, 2004. U.S. Pat. No. 6,115,718granted to Huberman et al. discloses a method for predicting documentaccess in a collection of linked documents featuring link probabilities,which may be interpreted as similarities in other long tail contexts.The method works by simulating a “law of surfing”, and achieves ascoring index that predicts the likelihood of access. U.S. Pat. No.7,734,641 granted to Kanigsberg et al. discloses a system forrecommendations, which is primarily based on the interpretation (usingthe semantic content of natural language) of user's searches, but alsouses the popularity index of the items.

In U.S. Pat. Nos. 7,949,627; 7,885,904; 7,792,815; 7,774,341; 7,657,526;and 7,529,741, all granted to Aravamudan et al., several methods aredisclosed to score the contents for each particular user in order toachieve better customized recommendations.

U.S. Patent Appl. Pub. No. 2010/0268661 by Levy et al. discloses amethod for building a recommendation system using two supervisedlearning techniques: categorical training, where recommended items arebased upon similar categories; and similar-to related training, wheresimilar items are used to find related items.

In “Factorization meets the neighborhood: a multifaceted collaborativefiltering model”, Proc. 14th ACM SIGKDD Int. Conf. on KnowledgeDiscovery and Data Mining (KDD'08), pp. 426-434, 2008, Koren advancesthe art of recommendation systems by merging the two most commonapproaches for exploiting collaborative filtering, namely factorization(i.e. profiling of users and products) and modeling of “neighborhoods”based on similarity. The author, who tested his methods on the datasetthat Netflix™ made available in 2006, recognizes the power ofneighborhood methods, as they work only on items and do not need tocompare users to items.

A different issue of concern here is the construction of a demand curvea priori, or the related problem of predicting the relative score of anew item in the universe. The method disclosed herein addresses thesetwo issues. One source of inspiration comes from the well-known utilityfunction theorem described in Von Neumann et al., “Theory of Games andEconomic Behavior”, Third Ed. (Princeton University Press, 1953), whichasserts that there exists a function that is able to reproduce theoutcomes of a set of pair-wise preferences between the items in the set.The other comes from the Elo rating system for ranking chess players, aprocess by which the relative skills between players end up producing ascoring curve that approximates the expected distribution (a Gaussian inthis case). See Elo, “The Rating of Chessplayers, Past and Present”(Arco, 1978; Ishi Press reprint, 2008) and Harkness, “Official ChessHandbook” (McKay, 1973). Invented by the Hungarian-born Americanphysicist and chess master Arpad Elo, the Elo method works by exchangingrating values between each two players according to the results of theirmatch, using a precise formula designed to reproduce a Gaussiandistribution. After a sufficiently large number of tournaments, theemergent curve of Elo ratings does reproduce the expected distribution.The Elo system was invented as an improved chess rating system, buttoday it is also used in many other multiplayer games and competitions.Even if statistical tests have shown that chess performance is notexactly normally distributed, the method is used with modified formulas,but still referred to as the Elo system.

There are not many studies directly related to the a priori modeling ofthe demand curve. U.S. Patent Appl. Pub. No. 2010/0121857 by Elmore etal. discloses an Internet-based method for ranking artists using apopularity profile. It is relevant here because it is a method thatturns dispersed information about preferences in popularity into aunified score that allows a ranking of all artists. In “RecommendationNetworks and the Long Tail of Electronic Commerce”, Sep. 1, 2010,available at SSRN: http://ssrn.com/abstract=1324064, Oestreicher-Singeret al. describe an approach to the study of the long tail demand curvefrom an interesting perspective: they analyze the effect of an existingsystem (recommendation networks) on the flattening of the curve.Alternatively, in “Open Mobile Platforms: Modeling the Long-Tail ofApplication Usage”, Fourth International Conference on Internet and WebApplications and Services, IEEE, pp. 112-118, May 2009, Verkasalostudies the modeling of the long tail demand curve for smart-phoneapplications, although from an empirical point of view.

SUMMARY

A main objective of this monetization procedure for long tail businessesis to provide a constructive method for obtaining the full distributionof scores, using only partial information about a few reference items(for which the score is known) and a quantitative method to expresssimilarity between items. In other words, the method disclosed hereinachieves an a priori modeling of the long-tailed demand curves usingonly partial information.

The system and method can constructively provide a monetizationprocedure for a long tail demand curve of market goods, services, orcontents through a channel such as the Internet or mobile devices, forwhich there exists a source providing economic scoring (sales,downloads, streaming hours, etc.). Using only the scorings for a fewreference items and a quantitative concept of similarity between theitems, the embodiments herein provide a procedure that constructivelydistributes the score from the reference items to the non-ranked ones,yielding the full scoring curve adjusted to a long tail law (power law).In order to build scores for non-ranked items, the method recursivelydefines relative preferences between items based on their similarity,thus constructing a utility-like function. The preferences are then usedwithin an iterative tournament strategy between the items, inspired inthe Elo method employed in the rating of professional chess players.This score can then be used to determine a recommendation strategy forcontent delivery that will have similarity as the base factor, yet allowimprovement and optimization of the monetization of the tail of the longtail distribution in a more controlled manner. The similarity orpreference-based measure underlying the invention as a base improves thepleasing of the receptor of the content.

DESCRIPTION OF THE DRAWINGS

FIG. 1 is an example of a basic long tail power law distribution graph.

FIG. 2 shows separation of the head and tail of the basic long tailpower law distribution graph of FIG. 1.

FIG. 3 is a close-up view of the tail portion of the graph in FIG. 2.

FIG. 4 is a further amplified view of the tail portion of the graph inFIG. 3.

FIG. 5 is a further amplified view of the tail portion of the graph inFIG. 4.

FIG. 6 shows a comparison of the tail portions shown in FIGS. 3, 4, and5.

FIG. 7 shows the basic input for a scoring procedure according to anembodiment herein.

FIG. 8 shows some of the components for the basic input fields of FIG. 7according to an embodiment herein.

FIG. 9 shows some specific input fields used for scoring media or webcontent according to an embodiment herein.

FIG. 10 illustrates a process step in a scoring procedure according toan embodiment herein.

FIG. 11 illustrates the process for handling similarity based recursivepreferences according to an embodiment herein.

FIG. 12 illustrates a process step in a scoring procedure according toan embodiment herein.

FIG. 13 illustrates a process step in a scoring procedure according toan embodiment herein.

FIG. 14 illustrates the process for handling similarity based recursivepreferences according to an embodiment herein.

FIG. 15 illustrates a process step in a scoring procedure according toan embodiment herein.

FIG. 16 illustrates a process step in a scoring procedure according toan embodiment herein.

DETAILED DESCRIPTION OF EXEMPLARY EMBODIMENTS

As popularized by the so-called Long Tail theory, the new era of on-lineretail allows businesses to enlarge their product catalog endlessly, atnearly zero-cost. Once the full range of different products is madeavailable to the people, it is an experimental fact that the demandcurves exhibit a long tail shape, as shown in FIG. 1, whereby the demandfor the lowest-ranked products does not fall sharply to zero (as it didin the pre-Internet era due to limited catalog offer, on the retailerspart). The gist of the theory is that businesses can now monetize thelong tail part of the demand. Moreover, the demand in the whole tail canactually add up to a percentage of sales that rivals the head of thecurve.

Referring to FIG. 1, for a given distribution, (such as by using a setof established parameters of the power law distribution as shown at 12)we depict the curve 14. FIG. 2 shows a separation of the curve 14 intotwo parts: head 24 and tail 26. In this manner, we can start to see thebehavior of the head 24 and tail 26. We can arbitrarily choose, for thepurpose of the example, the position of the value x separating the head24 and tail 26. In the example shown in FIG. 2, we have used the valueat x=1.9 thousand as the separation point, since it is the one thatmakes the areas under the curve (to the left and right of the x) equal.

It is well known that every time we approach larger values in the x-axisof the content objects or goods, in an ordered manner with regard to thedemand function, we can progressively see the tail of the tail (seeFIGS. 3, 4, and 5). FIG. 3 shows a longer portion of tail 26 of FIG. 2with a smaller scale x-axis. FIG. 4 shows a longer tail portion 43 ofFIG. 3 with an even smaller scale x-axis. FIG. 5 shows a longer tailportion 56 of FIG. 4 with yet an even smaller scale x-axis. Note thechange in scale size for the y-axis, as well. FIG. 6 shows the curvesfrom FIGS. 3, 4, and 5 together, in order to indicate the relativechange of scale in the x and y-axis, consecutively with scales rangingfrom 2 to 50 thousand in the x-axis and values from 0 to 25 in they-axis 26 (FIG. 3); from 11 to 75 thousand in the x-axis and values from0 to 2.75 in the y-axis 43 (FIG. 4); and from 33 to 175 thousand in thex-axis and values from 0 to 0.6 in the y-axis 56 (FIG. 5).

It is important to be able to model these curves correctly. However, themethod hereby proposed is not intended to fit existing sales data to amathematical model—after all, an on-line business already knows theircurrent sales rank and the full demand curve.

Referring to FIG. 7, the method actually constructs the demand curve forall objects or contents 78 (products, services, etc.), including thosefor which the ranking score 76 within the full universe is not knownyet. All that is required is that the objects in the universe are welldefined through a precise identity specification 72, a set of knownscores for some of the objects, and a quantifiable measure of similarity74 between all objects of the universe, from which we can generatescorings based on preferences calculated by similarity.

Embodiments of the method described herein are inspired on two ideas:the Von Neumann-Morgenstern utility theorem on the one hand, and the Elorating system (used originally in chess for ranking players worldwide,and today widely used in many sports and games) on the other.

The Von Neumann-Morgenstern utility theorem states that if we have a setof decision preferences among the objects of a given set, then thereexists a function on these objects that is able to reproduce thepreferences (we can think of this utility function as an absoluteranking function). In the problem described here, we do not havepreferences, but they are constructed based on the similarity measureconcept. Invented by the Hungarian-born American physicist and chessmaster Arpad Elo, the Elo method is aimed at the ranking of multipleplayers based on matches within tournaments engaging two players at atime. It works by exchanging rating values between each two playersaccording to the results of their match, using a precise formuladesigned to reproduce a scoring curve with a Gaussian distribution.After a sufficiently large number of tournaments, the emergentdistribution of Elo ratings does reproduce the distribution that isexpected theoretically.

The method described herein also works by iterating successive“tournaments” among objects of similar rank, but the precise mechanismfor the interaction (i.e. exchange) of the ratings is now designed toachieve a power-law decay curve rather than the Gaussian distributionmentioned above. Since the domain where this problem first appeared isthe media industry, we have dubbed this part of our method MELOtournaments, as in Media-Elo.

Let us describe now the general procedure in detail. As shown in FIG. 8,it is first required that we have three ingredients:

-   -   a) A universe of objects or content 88 (products, downloads,        etc.) with a well-defined identity 82, for which it is assumed        that the scoring/demand curve will follow a Long Tail law. They        will have to be very well defined with descriptors 82 a        intrinsic to the nature of the objects, metadata 82 b, tags 82        c, and others.    -   b) The scoring values 86 for a few objects, which will act as a        source of reference for the scores of the rest of the objects.        This can come from different sources 86 a, and they can have        different distributions 86 b. Different objects can be scored        using different scoring procedures 86 c. Embodiments herein will        treat the few objects with a Long Tail distribution (power law).    -   c) A quantitative scalar measure of similarity 84. The        similarities defined on all the content set will be used to        derive relative preferences among objects. These preferences are        used by the method to re-compute scorings in an Elo-like        process. Preferences could be derived from personal preferences        84 a, cultural preferences 84 b, and/or social networking        extracted information 84 c.

FIG. 9 shows a specific example on the wide variety in media contentthat can be found in streaming or downloading films or videos, such asthe parameters that can be found in the provider NETFLIX™. Moregenerally, the method described herein produces a long tail scoringcurve for any large set of objects, using only these elements: thescoring value of a few objects, which act as a source of referencevalues; a quantified measure of similarity between all objects; and theassumption that the scoring must follow a long tail decay as we progresstowards the lowest ranked (i.e. a power-law).

According to the method described herein, we will construct a procedureto propagate the known scoring values of the few elements to all thecontent population, by means of the Elo-like wide tournament, where the‘game’ is related to the proximity of the objects through the similaritymeasure between elements.

Let us denote with μ_(k), the score value of element k_(n) in ouruniverse. The demand curve is therefore given by the ordered set {μ_(k)_(n) }_(n=1 to N) where μ_(k) _(n) >μ_(k) _(n+1) for all n=1 to N. Thisis shown as curve 14 in FIG. 1, where one can see the decreasing rankingvalues in the y-axis as values increase in the x-axis.

The remaining Figures are used to illustrate the procedure in performingthe following steps:

Initialization: all objects k_(n) with unknown score value μ_(k) _(n)are assigned an arbitrary low score (e.g. zero); the reference objectsare assigned their known score values. Without loss of generality, itmay be assumed that these are all positive numbers, since if they werenot we could then translate (using lambda as the absolute value of theleast negative score, and translate by this lambda) and possibly scalethe scoring (“y” vertical) axis.

Step 1 (FIG. 10)—select a “tournament window”: a window 92 ofconsecutive objects within the current ordered set {μ_(k) _(n) } thatwill participate in the Elo-like tournament. The window 92, having awidth W, starts after some point k₀ 94. As discussed below, both thesize W of the window and the selection of the window location are notessential for the method to work. Randomly selected locations for thestart of the window after k₀ as well as the end of the window at k₀+W+196, determined by a fixed value of window width W of about ten to athousand objects, yield good results, demonstrating the robustness ofthe method.

Step 2 (FIG. 11)—use similarities among objects to construct the window.Compute the utility-function-like preferences for the items k_(n) 104 inthe window 92, using the similarity values according to the followingaveraging procedure: for every μ_(k) _(n) within the window 92, computeits temporary preference score μ_(k) _(n) ^(W) 108 as the average valueμ_(k) _(n) of over over the object and its nearest neighbors in theuniverse (see FIG. 12, 121). Note that the temporary preference scoreμ_(k) _(n) ^(W) 108 is initially based on the similarity of objects.μ_(k) _(n) ^(W) 108 represents the preference for an object in relationto the window 92. That is, for any given object k_(n)=A 112 within thewindow, there will be several neighbor objects 116. If we denote the setof nearest neighbors of object A by {A} 114, we calculate the preferencescore

$\mu_{A}^{W} = {\frac{1}{\# \left\{ A \right\}}{\sum\limits_{\{ A\}}\mu_{A}}}$

115. The set of nearest neighbor objects 116 to a given object A can befound using an arbitrarily chosen cut-off value ρ 118 for the similarityvalues that we have for the problem at hand (again, the method is robustagainst variations in this cut-off value). Then, the temporary scoresμ_(k) _(n) ^(W) 108 is used to reorder the subset {μ_(k) _(n)}_(n=1 to N) within the window 92 from least preferred to most preferredalong an increasing value for i 110. This results in the subset {μ_(k)_(n) }_(n=1 to N) shown in FIG. 13 in which the objects k_(n) 120 arereordered according to preference.

Step 3 (FIGS. 14 and 15)—redefine the scoring values according to thisMELO procedure, which is designed to achieve convergence and fit thedesired distribution of a long tail curve. Given k₀ 94 as a boundaryelement outside the window 92 with a preference score μ_(k) _(n) , beginby assigning a score

$\mu_{k_{1}} = {\left( {1 + \frac{E + 1}{R + k_{0}}} \right)\mu_{k_{0}}}$

124 to k₁ 122. Then compute the rest of the preference scores in thewindow recursively from k₁ 122 by making the score at each stage n+1based on the score calculated at stage n+1; that is, as shown in FIG.15, for k_(n+1) 125 its score as a function of the score for μ_(k) _(n)is defined as

$\mu_{k_{n + 1}} = {\left( {1 - \frac{E + 1}{R + k_{n}}} \right)\mu_{k_{n}}}$

128 until k_(n)=k_(N) or k_(N)=k₀+W 129. The values of E and R areadjusted a posteriori, once the procedure converges. Parameter E is theexponent of the power law, while R governs the rank value of the “x”axis (objects) of the long tail curve.

Step 4 (FIG. 16) is a renormalization step: all values in the universeμ_(k) _(n) →fμ_(k) _(n) 132 are adjusted using a normalization factor

$f = \frac{S}{\sum\limits_{n = {1{toN}}}\mu_{k_{n}}}$

134 designed so as to maintain a constant area or surface S under thecurve during the course of the whole procedure.

Repeat the procedure from step 1 to 4, until convergence in the values{μ_(k) _(n) } is reached.

This procedure has been found to be robust with respect to smallvariations in the choice of the size W of the tournament window 92.Larger windows may accelerate the convergence rate of the iterations,but this has to be weighed against the correspondingly larger 0(w log w)computational costs due to sorting. Additionally, the convergence is notgreatly affected by the particular strategy that is chosen for thelocation of the windows (index k₀): it is found that a randomly chosenindex k₀ works just as well as choosing a back-and-forth sliding window.Similarly, the computation of the temporary preference scores within thetournament window (see FIG. 12) is dependent upon some cut-off parameterρ 118 that needs to be chosen according to the particular typical valuesthat we have available for the similarity values. Again, it is foundthat the final results are not very sensitive to this cut-off value ρ118, provided we choose it sensibly: one should use a value big enoughso that objects have on average at least a few neighbors, but not so bigas to make the full universe 121 their neighbor.

Described herein is a Long Tail Monetization Procedure for contents orgoods on the internet, mobile devices, and other commerce platforms.Detailed below is a concrete implementation of the procedure on a twodimensional model, in order to show the feasibility of the industrialapplication of embodiments herein.

First, consider a geometric two-dimensional model in which the objectsunder study (our universe) are a set of N randomly chosen points (x_(k),y_(k)) within a rectangular domain of dimensions Xmax and Ymax. In otherwords,

9≦x_(k)≦X_(max)

0≦y_(k)≦Y_(max)

for k=1, . . . , N. Of course, once we have picked these N points wewill not change them during our procedure, since they are our universeof well-defined objects k_(n) (points). Their identities are uniquelydefined by their two-dimensional coordinates k_(n)=(x_(k) _(n) , y_(k)_(n) )

We now need to assume a known value for the scoring of some of thesepoints. We may randomly assign some starting values for the scoring μ toa fraction of the N points; these will become our “reference seeds” forthe final emergent scoring function. One may experiment the wholeprocedure with varying values of this fraction, as the results arerobust with respect to this value. In addition, for the purposes of thisembodiment, we will assume that the scoring values μ_(k) are positive.

Only one more ingredient is needed now, namely a quantitative measure ofsimilarity between points. For this, we will use the usual Euclideanmetric in two dimensions.

Again, using FIGS. 10-16, we can now start the constructive procedure tocompute the scoring curve for our universe, following these steps:

Initialization: all points k_(n)=(x_(k) _(n) , y_(k) _(n) ) with anunknown score value μ_(k) _(n) are assigned a zero score, while thereference objects are assigned their known score values.

Step 1—select a “tournament window”: a window 92 of consecutive pointswithin the current ordered set {μ_(k) _(n) } 95, on which the Elo-liketournament will take place. The window 92 starts after some point k₀ 94,and has a width W. As discussed below, both the size W of the window andthe selection of the window location are not essential for the method towork. Randomly selected locations for the start of the window after k₀as well as the end of the window 92 at k₀+W+1 96, determined by a fixedvalue of window width W of about ten to a thousand objects, yield goodresults, demonstrating the robustness of the method.

Step 2—compute the utility-function-like preferences for the items k_(n)104 in the window 92 using the similarity values according to thefollowing averaging procedure: for every μ_(k) within the window 92,compute its temporary preference score μ_(k) _(n) ^(W) 108 as theaverage value of μ_(k) _(n) over over the object and its nearestneighbors in the universe (see FIG. 12, 121). The set of nearestneighbors to a given object k_(n)=(x_(k) _(n) , y_(k) _(n) ) is to befound using an arbitrarily chosen cut-off value ρ 118 for thesimilarity. In this case, this should be a suitable distance intwo-dimensional space, so that the neighborhoods are neither too largenor too small considering the boundaries (Xmax, Ymax) where our universelives. Then, use these temporary scores μ_(k) _(n) ^(W) 108 to reorderthe subset {μ_(k) _(n) }_(n=1 to N) within the window 92 as shown inFIG. 13.

Step 3—calculate new scoring values according to this MELO procedure,which is designed to achieve convergence to a long tail curve. We havek₀ 94 as our first boundary element outside the window and its scoreμ_(k) ₀ . Start with element k₁ 122 by assigning the preference scoreμ_(k) ₁ =

$\left( {1 - \frac{E + 1}{R + k_{0}}} \right)\mu_{k_{0}}$

124 (FIG. 14). Then compute the rest of the scores in the window 92recursively starting from k₁ by making the score of k_(n+1) 125 afunction of the score of k_(n) 120 using the recursive formula

$\mu_{k_{n + 1}} = {\left( {1 + \frac{E + 1}{R + k_{n}}} \right)\mu_{k_{n}}}$

128 until k_(n)=k₀+W (see FIG. 15, 129). The values of E and R areadjusted a posteriori, once the procedure converges. Parameter E is theexponent of the power-law, while R governs the rank value of the “x”axis (objects) of the long tail curve.

Step 4—renormalization: all values in the universe μ_(k) _(n) →fμ_(k)_(n) 132 are adjusted using a normalization factor

$f = \frac{S}{\sum\limits_{n = {1{toN}}}\mu_{k_{n}}}$

134, designed so as to maintain a constant area or surface S under thecurve during the course of the whole procedure.

Repeat the procedure from step 1 to 4, until convergence in the values{μ_(k) _(n) }_(n=1 to N) is reached.

It is expected that any person skilled in the art can implement thedisclosed procedure on a computer, and verify the emergent scoring curvefor various realizations of the parameters in this example model. Thegeneralization of the procedure to real-world scenarios with otherdefinitions for the similarity measure should be evident to any personskilled in the art.

The invention has been described with references to specificembodiments. While particular values, relationships, materials and stepshave been set forth for purposes of describing concepts of theinvention, it will be appreciated by persons skilled in the art thatnumerous variations and/or modifications may be made to the invention asshown in the disclosed embodiments without departing from the spirit orscope of the basic concepts and operating principles of the invention asbroadly described. It should be recognized that, in the light of theabove teachings, those skilled in the art could modify those specificswithout departing from the invention taught herein. Having now fully setforth certain embodiments and modifications of the concept underlyingthe present invention, various other embodiments as well as potentialvariations and modifications of the embodiments shown and describedherein will obviously occur to those skilled in the art upon becomingfamiliar with such underlying concept. It is intended to include allsuch modifications, alternatives and other embodiments insofar as theycome within the scope of the appended claims or equivalents thereof. Itshould be understood, therefore, that the invention might be practicedotherwise than as specifically set forth herein. Consequently, thepresent embodiments are to be considered in all respects as illustrativeand not restrictive.

The corresponding structures, materials, acts, and equivalents of allmeans or step plus function elements in the claims below are intended toinclude any structure, material, or act for performing the function incombination with other claimed elements as specifically claimed. Thedescriptions of the various embodiments herein have been presented forpurposes of illustration, but are not intended to be exhaustive orlimited to the embodiments disclosed. Many modifications and variationswill be apparent to those of ordinary skill in the art without departingfrom the scope and spirit of the described embodiments. The terminologyused herein was chosen to best explain the principles of theembodiments, the practical application or technical improvement overtechnologies found in the marketplace, or to enable others of ordinaryskill in the art to understand the embodiments disclosed herein.

1. A method of determining monetization for a long tail demand curve,said demand curve comprising an ordered set of objects, at least someobjects in said ordered set having a known preference score value, saidmethod comprising: for all objects in said ordered set not having apreference score value, assigning an arbitrary low preference scorevalue, using a computerized device; selecting a window of consecutiveobjects from said ordered set of objects, using said computerizeddevice, at least some objects in said window having a known preferencescore value; calculating a temporary preference score for each object insaid window not having a preference score value based on its similarityto a nearest object in said window having a known preference scorevalue, using said computerized device; and reordering all objects insaid window based on said temporary preference score and said knownpreference score, using said computerized device.
 2. The method of claim1, further comprising: for all objects in said window, calculating a newscoring value using a power-law exponential equation, using saidcomputerized device.
 3. The method of claim 2, said power-lawexponential equation comprising:$\mu_{k_{1}} = {\left( {1 - \frac{E + 1}{R + k_{0}}} \right)\mu_{k_{0}}}$where k₀ comprises a boundary element outside said window, μ_(k) ₀comprises said scoring value for said boundary element k₀, E comprisesan exponent of said power-law, and R governs a rank value of objectsalong said long tail demand curve.
 4. The method of claim 3, furthercomprising recursively calculating a scoring value for each object insaid window starting from element k₁ using a recursive formula$\mu_{k_{{n + 1}\;}} = {\left( {1 + \frac{E + 1}{R + k_{n}}} \right)\mu_{k_{n}}}$until k_(n)=k_(o)+W, using said computerized device, where k₀ comprisesa boundary element outside said window, k_(n) comprises a next elementin said window, W comprises a number of elements in said window, μ_(k)_(n) comprises said scoring value for element k_(n), μ_(k) _(n+1)comprises said scoring value for element k_(n+1), E comprises anexponent of said power-law, and R governs a rank value of objects alongsaid long tail demand curve.
 5. The method of claim 2, furthercomprising: normalizing said score values for all objects in saidordered set of objects, using said computerized device.
 6. The method ofclaim 5, said normalizing comprising using a normalization factordesigned to maintain a constant area under said long tail demand curve.7. The method of claim 6, said normalization factor comprising:$f = \frac{S}{\sum\limits_{n = {1{toN}}}\mu_{k_{n}}}$ where fcomprises said normalization factor, μ_(k) _(n) comprises said scoringvalue for each element k_(n) in said window, S comprises said area undersaid long tail demand curve, and N comprises a number of objects in saidwindow.
 8. The method of claim 1, said calculating a temporarypreference score comprising using an equation$\mu_{A}^{W} = {\frac{1}{\# \left\{ A \right\}}{\sum\limits_{\{ A\}}\mu_{A}}}$where μ_(A) ^(W) comprises said temporary preference score in saidwindow W, {A} comprises a set of objects within a specified distancefrom an object A in said window W, μ_(A) comprises said known preferencescore value for element A in said window W, and #{A} comprises a numberof objects in said set {A}.
 9. The method of claim 1, said windowcomprising more than ten objects.
 10. The method of claim 1, said windowcomprising less than a thousand objects.
 11. A computer implementedmethod of determining monetization for a long tail demand curve, saidmethod comprising: providing an ordered set of objects, at least someobjects in said ordered set having a known preference score value, usinga computerized device; selecting a first window of consecutive objectsfrom said ordered set of objects, using said computerized device, atleast some objects in said first window having a known preference scorevalue; calculating a temporary preference score for each object in saidfirst window not having a preference score value based on its similarityto a nearest object in said first window having a known preference scorevalue, using said computerized device; reordering all objects in saidfirst window based on said temporary preference score and said knownpreference score, using said computerized device; and calculating a newscoring value for all objects in said first window, using a power-lawexponential equation, using said computerized device.
 12. The computerimplemented method of claim 11, further comprising: selecting a secondwindow of consecutive objects from said ordered set of objects, usingsaid computerized device, at least some objects in said second windowhaving a known preference score value; recalculating a temporarypreference score for each object in said second window not having apreference score value, using said computerized device; reordering allobjects in said second window based on said temporary preference scoreand said known preference score, using said computerized device; andrecalculating a new scoring value for all objects in said second window,using a power-law exponential equation, using said computerized device.13. The computer implemented method of claim 11, said power-lawexponential equation comprising:$\mu_{k_{1\;}} = {\left( {1 - \frac{E + 1}{R + k_{0}}} \right)\mu_{k_{0}}}$where k₀ comprises a boundary element outside said first window, μ_(k) ₀comprises said scoring value for said boundary element k₀, E comprisesan exponent of said power-law, and R governs a rank value of objectsalong said long tail demand curve.
 14. The computer implemented methodof claim 13, further comprising recursively calculating a scoring valuefor each object in said first window starting from element k₁ using arecursive formula$\mu_{k_{n + 1}} = {\left( {1 + \frac{E + 1}{R + k_{n}}} \right)\mu_{k_{n}}}$until k_(n)=k₀+W, using said computerized device, where k₀ comprises aboundary element outside said first window, k_(n) comprises a nextelement in said first window, W comprises a number of elements in saidfirst window, μ_(k) _(n) comprises said scoring value for element k_(n),μ_(k) _(n+1) comprises said scoring value for element k_(n+1), Ecomprises an exponent of said power-law, and R governs a rank value ofobjects along said long tail demand curve.
 15. The computer implementedmethod of claim 11, further comprising: normalizing said score valuesfor all objects in said ordered set of objects, using said computerizeddevice.
 16. The computer implemented method of claim 15, saidnormalizing comprising using a normalization factor designed to maintaina constant area under said long tail demand curve.
 17. The computerimplemented method of claim 16, said normalization factor comprising:$f = \frac{S}{\sum\limits_{n = {1{toN}}}\mu_{k_{n}}}$ where fcomprises said normalization factor, μ_(k) _(n) comprises said scoringvalue for each element k_(n) in said first window, S comprises said areaunder said long tail demand curve, and N comprises a number of objectsin said first window.
 18. The computer implemented method of claim 11,said calculating a temporary preference score comprising using anequation$\mu_{A}^{W} = {\frac{1}{\# \left\{ A \right\}}{\sum\limits_{\{ A\}}\mu_{A}}}$where μ_(A) ^(W) comprises said temporary preference score in said firstwindow W, {A} comprises a set of objects within a specified distancefrom an object A in said first window W, μ_(A) comprises said knownpreference score value for element A in said first window W, and #{A}comprises a number of objects in said set {A}.
 19. The computerimplemented method of claim 11, said first window comprising more thanten objects.
 20. The computer implemented method of claim 11, said firstwindow comprising less than a thousand objects.